La Houille Blanche
Number 7-8, Novembre 1982
|Page(s)||571 - 578|
|Published online||01 November 2009|
Modèle d'écoulement dans les bâches fronto-spirales
A model of the flow in fronstospiral casing
Société Neyrpic Grenoble
Up to now the hydraulic conception of the spiral casing used in low head KAPLAN turbines was solved by experimental tests. These approach is undoubtedly time and money consuming. As 20 to 30 % of the losses are located in front of the runner it is very important to optimize the casing and the stay-vanes to insure a correct incoming flow to the wicketgates. The main objective of this work was thus to develop a theoretical approach of the flow in order to get an homogeneous peripheral velocity distribution at the exit of the stayvanes. The method is based on the solution of a flow field problem. Making use of the following assumptions, inviscid, irrotationnal and quasi-3D flow the governing equation based on the stream function is of the Poisson type. Using a body fitted coordinate system the second order equation is discretised by finite differences. The numerical solution is than carried using an Alternating Direction Implicit technique known as Approximate Factorisation 1. The computation starts without stay-vanes imposing uniform flow rate at the exit of the casing. This Diricklet boundary condition leads to a solution where the expected uniform prewhirl is not fullfiled. A finite number of stay vanes are than introduced in the field in order to get the correct flow deflection. At the mesh points located on the presumed blade location a distribution of bound vortex is applied, the vorticity is updated until the given prewhirl condition is met. However at the same time the nodal value of the stream function is enforced at the trailing edge of the stay-vanes to maintain the constant peripheraI flow rate and the blade position is changed iteratively in order to correspond with a streamline. At convergence the computation provides the shape and the load of each stay-vane required to obtain the prescribe uniform flow at the wicket-gates inlet. Numerical solutions are presented for a typical KAPLAN casing and compared with available experimental and theorical results.
© Société Hydrotechnique de France, 1982
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